We investigate different asymptotic regimes for Vlasov equations modeling the evolution of a cloud of particles in a turbulent flow. In one case we obtain a convection or a convection-diffusion effective equation on the concentration of particles. In the second case, the effective model relies on a Vlasov-Fokker-Planck equation.
Mots-clés : fluid-particles interaction, hydrodynamic limits, turbulence effects
@article{M2AN_2004__38_4_673_0,
author = {Goudon, Thierry and Poupaud, Fr\'ed\'eric},
title = {On the modeling of the transport of particles in turbulent flows},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {673--690},
publisher = {EDP-Sciences},
volume = {38},
number = {4},
year = {2004},
doi = {10.1051/m2an:2004032},
mrnumber = {2087729},
zbl = {1079.76037},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2004032/}
}
TY - JOUR AU - Goudon, Thierry AU - Poupaud, Frédéric TI - On the modeling of the transport of particles in turbulent flows JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2004 SP - 673 EP - 690 VL - 38 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2004032/ DO - 10.1051/m2an:2004032 LA - en ID - M2AN_2004__38_4_673_0 ER -
%0 Journal Article %A Goudon, Thierry %A Poupaud, Frédéric %T On the modeling of the transport of particles in turbulent flows %J ESAIM: Modélisation mathématique et analyse numérique %D 2004 %P 673-690 %V 38 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2004032/ %R 10.1051/m2an:2004032 %G en %F M2AN_2004__38_4_673_0
Goudon, Thierry; Poupaud, Frédéric. On the modeling of the transport of particles in turbulent flows. ESAIM: Modélisation mathématique et analyse numérique, Tome 38 (2004) no. 4, pp. 673-690. doi : 10.1051/m2an:2004032. http://www.numdam.org/articles/10.1051/m2an:2004032/
[1] , Limites fluides pour des modèles cinétiques de brouillards de gouttes monodispersés. C. R. Acad. Sci. 331 (2000) 651-654. | Zbl
[2] , Limite semi-classique de transformées de Wigner dans des milieux périodiques ou aléatoires. Thèse Université de Nice-Sophia Antipolis (Novembre 2002).
[3] and, The dynamics of aerocolloidal systems. Pergamon Press (1970).
[4] and, Dynamic theory of suspensions with Brownian effects. SIAM J. Appl. Math. 43 (1983) 885-906. | Zbl
[5] and, Solutions of a kinetic stochastic equation modeling a spray in a turbulent gas flow. Math. Models Methods Appl. Sci. 7 (1997) 239-263. | Zbl
[6] , About the modeling of complex flows by gas-particles methods, Proceedings of the workshop “Trends in Numerical and Physical Modeling for Industrial Multiphase Flows”, Cargèse, France (2000).
[7] and, Limites visqueuses pour des systèmes de type Fokker-Planck-Burgers unidimensionnels. C. R. Acad. Sci. 332 (2001) 863-868. | Zbl
[8] and, Work in preparation. Personal communication.
[9] and, Kinetic model for the motion of compressible bubbles in a perfect fluid. Eur. J. Mech. B/Fluids 21 (2002) 469-491. | Zbl
[10] , in From kinetic to macroscopic models in Kinetic equations and asymptotic theory, B. Perthame and L. Desvillettes Eds., Gauthier-Villars, Ser. Appl. Math. 4 (2000) 41-121. | Zbl
[11] , Asymptotic problems for a kinetic model of two-phase flow. Proc. Royal Soc. Edimburgh 131 (2001) 1371-1384. | Zbl
[12] , and, Hydrodymamic limit for the Vlasov-Navier-Stokes system: Light particles regime. Preprint.
[13] , and, Hydrodymamic limit for the Vlasov-Navier-Stokes system: Fine particles regime. Preprint.
[14] , Global existence and large time behaviour of solutions for the Vlasov-Stokes equations. Japan J. Ind. Appl. Math. 15 (1998) 51-74. | Zbl
[15] , and, On the motion of dispersed balls in a potential flow: a kinetic description of the added mass effect. SIAM J. Appl. Math. 60 (1999) 61-83. | MR | Zbl
[16] , Large time concentrations for solutions to kinetic equations with energy dissipation. Comm. Partial Differential Equations 25 (2000) 541-557. | MR | Zbl
[17] , Macroscopic limit of Vlasov type equations with friction. Ann. IHP Anal. Non Linéaire 17 (2000) 651-672. | EuDML | Numdam | MR | Zbl
[18] and, in Notes on mathematical problems on the dynamics of dispersed particles interacting through a fluid in Modeling in applied sciences, a kinetic theory approach, N. Bellomo and M. Pulvirenti Eds., Birkhäuser (2000) 111-147. | MR | Zbl
[19] and, Simplified models for turbulent diffusion: Theory, numerical modeling, and physical phenomena. Physics Reports 314 (1999) 237-574. | MR
[20] , Stochastic Liouville equations. J. Math. Phys. 4 (1963) 174-183. | MR | Zbl
[21] and, Electric turbulence in a plasma subject to a strong magnetic field. Preprint. | MR | Zbl
[22] , Statistical properties and numerical implementation of a model for droplets dispersion in a turbulent gas. J. Comp. Phys. 83 (1989) 345-360. | Zbl
[23] and, Classical and quantum transport in random media. J. Math. Pures Appl. 82 (2003) 711-748. | MR | Zbl
[24] and, Kinetic theory for bubbly flows I, II. SIAM J. Appl. Math. 56 (1996) 327-371. | Zbl
[25] , A review of mathematical topics in collisional kinetic theory, in Handbook of mathematical fluid mechanics, S. Friedlander and D. Serre Eds., North-Holland (2002). | MR | Zbl
[26] , Combustion theory. Benjamin Cummings Publ., 2nd edn. (1985).
[27] , A statistical model of particle transport and heat transfer in turbulent shear flows. Phys. Fluids 11 (1999) 1521-1534. | Zbl
Cité par Sources :
